Hexagonal mosaic links generated by saturation

Abstract

Square mosaic knots have many applications in algebra, such as modeling quantum states. In this paper, we extend mosaic knot theory to a theory of hexagonal mosaic links, which are links embedded in a plane tiling of regular hexagons. We investigate hexagonal mosaic links created from particular patches of hextiles with a high number of crossings, which we describe as saturated diagrams. Considering patches of varying size and shape, we compute the number of link components that are produced in these saturated diagrams and for special families we identify the knot types of the components. Finally, we discuss open questions relating to saturated diagrams.